Nonlinear Fiber Research Articles

Dispersion Engineering for Advanced Temporal Imaging Modalities

Temporal imaging provides a promising platform for ultrafast signal processing in both spectral and temporal domains. Most temporal imaging systems consist of time-lens and temporal dispersion; while optical fibers are desirable to achieve the dispersion component by virtue of their acceptable losses. On the other hand, parametric mixing-based time-lens is commonly used in temporal imaging thanks to the high modulation depth. In those situations, highly nonlinear fiber (HNLF) is used as the nonlinear medium. However, third-order dispersion (TOD) exists in commercial fibers will incur temporal aberration on the system. For instance, the inherent dispersion in HNLF decreases the conversion bandwidth of the parametric process, which restricts the performance of time-lens. In this article, we present our recent efforts in dispersion engineering for temporal imaging systems, both in the temporal dispersion and the nonlinear medium. All these efforts could inspire more innovative applications of temporal imaging modalities in the future.

DSP optimization technique based on deep learning to account for the effects of fiber nonlinearity

The first section of this work is the classification of digital signal processing (DSP) techniques for adjusting, minimizing, and utilizing fiber nonlinearities in coherent fiber optic transmission systems. Then, different experimental optimization methods based on the Volterra series of Deep Neural Networks (DNN) and the Digital Back Propagation (DBP) methods are contrasted with the aid of specific instances. Concrete examples reinforce the techniques. The findings demonstrate the viability of a DSP strategy using deep learning for inexpensive optical comms, resulting in significant performance gains and computational efficiencies. The optimal DSP, it is further determined, should balance minimizing transmission flaws with minimizing additional distortions brought on by ineffective linear or nonlinear correction steps as a result of in-line amplifier noise. It is demonstrated that, in addition to improving system performance, machine learning (ML) improves analytical reasoning, provides deeper mathematical comprehension of fiber nonlinearity correction, and advances theoretical knowledge in related fields.

Exact chirped solutions for the NLSE having Kudryashov’s law with dual form of generalized non-local nonlinearity

This paper devotes to investigating the chirped solutions for the nonlinear Schrödinger equation with Kudryashov’s law with dual form of generalized non-local nonlinearity in optical fibers. By implementing the trial equation method and the complete discriminant system for polynomial method, we obtain nineteen exact chirped solutions, whose types include elliptic function doubly-periodic solutions, solitary wave solutions and singular solutions. After selecting specific parameters, 2D and 3D graphs of several typical solutions are drawn to demonstrate their accurate physical behaviors. These solutions recovered abundant patterns of the chirped wave propagations of the model.

Quantum key distribution via frequency translation in a nonlinear optical fiber

Quantum key distribution via frequency translation in a nonlinear optical fiber

Design of dispersion-flattened photonic crystal fiber with 800 nm wide low-dispersion band

We propose a new design for a dispersion-flattened photonic crystal fiber with 800 nm wide low-dispersion band by employing the imaginary-distance beam propagation method and the transparent boundary condition using BeamPROP simulation software. The chromatic dispersion of the fiber is −1.4 to 4.8 ps/nm·km in an 800 nm wavelength range of 1.1–1.9 μm. The effective mode area at a wavelength of 1.55 μm is 12.2 μm2 and the fiber can be easily joined to conventional nonlinear optical fiber with a small core. The calculated effective index is extremely linear via the wavelength, and the decision coefficient with an approximately straight function is 0.999996, this means the waveguide dispersion of the proposed PCF completely compensates for the material dispersion curves.

Exact soliton solutions and stability analysis to (3 + 1)-dimensional nonlinear Schrödinger model

In this research, a dynamical (3 + 1)-dimensional nonlinear Schrödinger model (NLSM) is under consideration which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This aforementioned model has been widely applied in Bose–Einstein condensates, nonlinear optical fiber communication plasma physics, hydrodynamics, elastic media and other diversified areas of mathematical physics and engineering. This study has two main objectives. Firstly, to obtain some novel solutions in the shape of singular, dark, periodic and plane wave solutions that are innovative and not previously found in the literature. Secondly, an amended extended tanh-function method with modulation instability (MI) is used for this model. As far as we know, this has never been investigated in this manner. The 2-D, 3-D and contour plots have been defined using the required parametric values to support the results of physical compatibility. According to the examined results, the method used in this study to retrieve consisting and conventional solutions is efficient and more immediate in computing and can be thought of as a useful tool in resolving more difficult problems that arise in the field of engineering, physics, mathematics and fiber optics.

Simultaneous sensing of temperature and strain with enhanced performance using forward Brillouin scattering in highly nonlinear fiber.

Simultaneous temperature and strain sensing has been demonstrated for the first time to our knowledge by using forward Brillouin scattering (FBS) in a highly nonlinear fiber (HNLF). It is based on different responses of radial acoustic modes R0,m and torsional-radial acoustic modes TR2,m to the temperature and strain. High-order acoustic modes with large FBS gain in an HNLF are chosen to improve the sensitivity. To reduce the measurement error, a method to select the best mode combination with the lowest measurement errors is proposed and demonstrated by both simulation and experiment. Three mode combinations have been used for both temperature and strain sensing, and by using the mode combination (R0,18, TR2,29), the lowest temperature and strain errors of 0.12°C/39 µɛ have been achieved. Compared with sensors using backward Brillouin scattering (BBS), the proposed scheme only requires frequency measurement around 1 GHz, which is cost-effective without the need for a ∼10-GHz microwave source. Moreover, the accuracy is enhanced since the FBS resonance frequency and spectrum linewidth are much smaller than those of BBS.

Reconfigurable all-optical format conversion for 16QAM/8QAM by employing PSA in HNLF.

Extensive investigations are undertaken on the feasibility of utilizing phase sensitive amplification (PSA) in highly nonlinear fiber (HNLF) to achieve a reconfigurable 16QAM/8QAM all-optical format conversion for optical data center networks. A comprehensive theoretical model is developed and subsequently verified, based on numerical simulations undertaken to explore the effectiveness of the nonlinear effects of phase insensitive amplification, PSA, and self phase modulation for the proposed all-optical format conversion scheme. It is demonstrated that the proposed scheme can achieve a reconfigurable all-optical format conversion from a 16QAM signal to two quadrature phase shift keying (QPSK) signals or from an 8QAM signal to one QPSK signal and one binary phase shift keying signal with data rates of 92Gbps and 69Gbps for 16QAM and 8QAM signals, respectively.

Fiber-optic frequency comb generation using low-seed power FWM and Brillouin-assisted power equalization.

In this paper, we experimentally demonstrate an all-fiber broadband tunable optical frequency comb (OFC) operating in the C-band. The OFC is generated by broadening a power-equalized stimulated Brillouin scattering (SBS)-based seed comb (SBS-OFC) using four-wave mixing (FWM) in a highly nonlinear fiber (HNLF). The seed SBS-OFC is obtained from a pump and Stokes power recycling cavity, which yields ≈15 comb lines with 10.8GHz line spacing having 16dBm average power. The seed SBS-OFC is further power-equalized by a Brillouin-assisted power equalization (BAPE) technique to minimize the high pump contribution at the recycling cavity output. The power-equalized seed SBS-OFC, which has low-power of -4.5d B m at the BAPE cavity output, is propagated down a dual-pass 200m dispersion flattened HNLF. At the HNLF output, we obtain ≈140 comb lines within a 12nm bandwidth having 10.8GHz line spacing. We demonstrate wavelength tunability over a span of 35nm by using a tunable laser source as the Brillouin pump. We also observe and measure a secondary OFC generated during the power-equalization process by placing a 10% coupler inside the BAPE cavity. Our experimental results closely match the trends obtained in the simulation.

An extension to the enhanced Gaussian noise model in optical bus considering various links spectrum

Physical layer impairment modeling has considerably influenced optical networking in optimizing resource allocation for fulfilling a required quality of transmission. Among these impairments, the modeling of optical fiber non-linearity has enjoyed widespread applications by vendors and network operators, giving rise to the two well established Gaussian noise (GN) and enhanced Gaussian noise (EGN) models. In this work, we introduce an extension to the EGN model for a point-to-point bus transmission, where a demand is not typically routed over a single link. More specifically, we assume that a lightpath is routed over a bus and multiple interferers occasionally add and drop along the links, resulting in a mixture of coherent and incoherent non-linear propagation. We propose a mathematical formulation in the optical bus scenario, taking into account the spectrum variation of the links along the bus. To more accurately address their mutual statistical correlation in non-linear interference estimation, we make use of extra lightpath information. Along with presenting the new formulation, we modify the non-linear link function to include the spectrum variation of a lightpath links. The exploited optical bus topology is capable of approximating a real network lightpaths to enable design optimization of optical networks. Our numerical results show approximately 0.4 dB and 0.6 dB improvements versus the GN and EGN models in long bus scenarios with moderate number of channels and lightpaths, and around 0.3 dB minimum improvement.

Joint PMD Tracking and Nonlinearity Compensation With Deep Neural Networks

Overcoming fiber nonlinearity is one of the core challenges limiting the capacity of optical fiber communication systems. Machine learning based solutions such as learned digital backpropagation (LDBP) and the recently proposed deep convolutional recurrent neural network (DCRNN) have been shown to be effective for fiber nonlinearity compensation (NLC). Incorporating distributed compensation of polarization mode dispersion (PMD) within the learned models can improve their performance even further but at the same time, it also couples the compensation of nonlinearity and PMD. Consequently, it is important to consider the time variation of PMD for such a joint compensation scheme. In this paper, we investigate the impact of PMD drift on the DCRNN model with distributed compensation of PMD. We propose a transfer learning based selective training scheme to adapt the learned neural network model to changes in PMD. We demonstrate that fine-tuning only a small subset of weights as per the proposed method is sufficient for adapting the model to PMD drift. Using decision directed feedback for online learning, we track continuous PMD drift resulting from a time-varying rotation of the state of polarization (SOP). We show that transferring knowledge from a pre-trained base model using the proposed scheme significantly reduces the re-training efforts for different PMD realizations. Applying the hinge model for SOP rotation, our simulation results show that the learned models maintain their performance gains while tracking the PMD.

Deep Learning-Aided Perturbation Model-Based Fiber Nonlinearity Compensation

Fiber nonlinearity effects cap achievable rates and ranges in long-haul optical fiber communication links. Conventional nonlinearity compensation methods, such as perturbation theory-based nonlinearity compensation (PB-NLC), attempt to compensate for the nonlinearity by approximating analytical solutions to the signal propagation over optical fibers. However, their practical usability is limited by model mismatch and the immense computational complexity associated with the analytical computation of perturbation triplets and the nonlinearity distortion field. Recently, machine learning techniques have been used to optimise parameters of PB-based approaches, which traditionally have been determined analytically from physical models. It has been claimed in the literature that the learned PB-NLC approaches have improved performance and/or reduced computational complexity over their non-learned counterparts. In this paper, we first revisit the acclaimed benefits of the learned PB-NLC approaches by carefully carrying out a comprehensive performance-complexity analysis utilizing state-of-the-art complexity reduction methods. Interestingly, our results show that least squares-based PB-NLC with clustering quantization has the best performance-complexity trade-off among the learned PB-NLC approaches. Second, we advance the state-of-the-art of learned PB-NLC by proposing and designing a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fully learned</i> structure by adopting the noiseless Manakov equation as the channel propagation model. We apply a bi-directional recurrent neural network for learning perturbation triplets that are alike those obtained from the analytical computation and are used as input features for the neural network to estimate the nonlinearity distortion field. Finally, we demonstrate through numerical simulations that our proposed fully learned approach achieves an improved performance-complexity trade-off compared to the existing learned and non-learned PB-NLC techniques.

Modulation instability in inhomogenous nonlinear optical fiber

Modulation instability in inhomogenous nonlinear optical fiber

Some specific optical wave solutions and combined other solitons to the advanced (3+1)-dimensional Schrödinger equation in nonlinear optical fibers

Some specific optical wave solutions and combined other solitons to the advanced (3+1)-dimensional Schrödinger equation in nonlinear optical fibers

Simultaneous OSNR and chromatic dispersion monitoring based on optical tones power ratio

A novel technique is proposed for simultaneous monitoring of optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD). The scheme is based on the cross-phase modulation effect in a highly nonlinear fiber, which induces a change in the optical tones according to the impairments. The power ratio of the optical tones at two separate frequencies is utilized for monitoring. Improvements in the maximum measurable OSNR, CD and dynamic range can be obtained using only the clock tone for the non-return-to-zero, return-to-zero with a 50% duty cycle differential quadrature phase-shift keying, differential phase-shift keying and on-off keying signals at 80 Gb/s. For the return to zero differential quadrature phase shift keying (RZ-DQPSK) system, the OSNR of 4–40 dB can be monitored with a 36.73 dB dynamic range, and a chromatic dispersion of 0–117 ps/nm can be monitored with a 48.68 dB dynamic range. A correlation is built to describe the relationship of the power ratio with the OSNR and chromatic dispersion which has a root-mean-squared error of 1.41. The delay group dispersion insensitivity, the impact of the input signal power, and the filter selection are investigated. The design enables accurate monitoring, simple operation and may be used in a wide range.

Initialized autoencoders to find constellations robust to residual laser phase noise

Autoencoder (AE) has been used to find quadrature amplitude modulation (QAM) constellations robust to optical impairments, such as residual laser phase noise or fiber nonlinearities. We examine AE for constellations for fiber links with residual phase noise following phase recovery. We study 1) improved constellations via AE neural network (NN) initialization, 2) bit-to-symbol mappings for AE constellations, and 3) performance enhancement from the AE decoder as a detection algorithm. We compare our performance to several other phase-noise-optimized constellations, using an identical phase recovery method for fair comparison. We confirm the improved performance of our constellations experimentally as well as via simulation. Our AE initialization technique (using previous constellations found experimentally, empirically, numerically, etc.) is shown to improve constellations for 16QAM and 64QAM. A bit-to-symbol mapping is essential to benefit fully from AE constellations, but is intractable to optimize. We use an ad hoc approach that derives mappings from our initialization constellations. Our AE initialization technique leads to performance improvements over the previous QAM constellations under all metrics: generalized mutual information (GMI), bit error rate (BER) and symbol error rate (SER). We examine the gap between BER and SER due to non-optimal bit-to-symbol mappings. The AE approach to constellation design has as a byproduct an optimized detector: the AE decoder. We quantify the improvement of this detector over the classic maximum likelihood detection that neglects phase noise.

A Numerical Mode Matching (NMM) Method for Optical Fibers With Kerr Nonlinearity

Recently, the reshaping of the transverse light field profile in nonlinear multimode fibers (MMFs) has attracted great attentions. However, the electromagnetic (EM) fields in such nonlinear media cannot be easily and accurately calculated by using the traditional computational electromagnetics methods due to the nonlinearity of Kerr optical materials in graded-index (GRIN) MMFs. The iterative division method based on the 2.5-D spectral element numerical mode matching (SNMM) method is developed to address this problem. The SNMM method is a semi-analytical method, which can effectively reduce the computational costs to obtain highly accurate solutions. Starting from the numerical results of SNMM, the iterative division method solves electromagnetic fields of the linear-to-nonlinear transition process together iteratively. In this work, several improvements are proposed to extend the SNMM for Kerr optical nonlinear MMFs. The governing equations with anisotropic permittivity with Kerr optical nonlinear media are established in the cylindrical coordinate system. The absorbing boundary condition (ABC) is introduced to replace the perfectly matched layer (PML) so that the eigenmodes of a waveguide can be obtained accurately. Numerical results show the validity, accuracy and advantages of the proposed method in simulated MMFs.

A two-color dual-comb system for time-resolved measurements of ultrafast magnetization dynamics using triggerless asynchronous optical sampling.

We report on an Er-doped fiber (EDF)-laser-based dual-comb system that allows us to perform triggerless asynchronous optical sampling pump-probe measurements of ultrafast demagnetization and spin precession in magnetic materials. Because the oscillation frequencies of the two frequency-comb light sources are highly stabilized, the pulse-to-pulse timing jitter is sufficiently suppressed, and data accumulation without any trigger signals is possible. To effectively induce spin precession in ferromagnetic thin films, the spectral bandwidth of the output of one of the EDF frequency comb sources is broadened by a highly nonlinear fiber and then amplified at a wavelength of about 1030nm by a Yb-doped fiber amplifier. The output of the other frequency comb source is converted to about 775nm by second harmonic generation. We used this system to observe ultrafast demagnetization and spin precession dynamics on the picosecond and nanosecond time scales in a permalloy thin film. This time-domain spectroscopy system is promising for the rapid characterization of spin-wave generation and propagation dynamics in magnetic materials.

Optimal Design of Eigenvalues for the Full-Spectrum Modulated Nonlinear Frequency Division Multiplexing Transmission System

Nonlinear frequency division multiplexing (NFDM) system is an optional candidate to overcome the fiber nonlinearity limit. A full-spectrum modulated NFDM system, modulating data on combined continuous spectrum (CS) and discrete spectrum (DS) together, was proposed in recent years to improve the data rates and spectral efficiency (SE) by exploiting all the degrees of freedom offered in the nonlinear spectrum. However, the selection of discrete eigenvalues greatly affects the performance of both CS and DS. Designing appropriate eigenvalues of DS is an important issue to ensure the high SE and excellent performance of the system. In this paper, we discussed the selcection principle of eigenvalues and analyzed it from multiple perspectives, 11 eigenvalues with 64-quadrature amplitude modulation (64QAM) are selected for DS. Besides optimizing the eigenvalues at the transmitter, the linear minimum mean-square estimate (LMMSE) method was used at the receiver to furtherly improve the performance of DS. Through the numerical simulation, a 113 Gb/s (SE of 2.8 bits/s/Hz) full-spectrum modulated NFDM system was set up and transmitted 1120 km distance, where the Q-factors of both CS and DS are above the hard-decision forward error correction (HD-FEC) threshold. The results provide a way to design an efficiently full-spectrum modulated NFDM system.

Pulse-shaped high-energy and high-average-power fiber laser in the nanosecond regime.

A high-energy and high-average-power pulsed fiber laser has been investigated in a master oscillator power amplifier (MOPA) configuration seeding with a diode laser at a programmed pulse duration of ∼250ns. The fiber amplifier successfully demonstrates the pulse with 21.4 mJ at the repetition rate of 50 kHz and a maximum average output power of 1535 W with a slope efficiency of 81.6% at 250 kHz. To overcome fiber nonlinearities such as stimulated Raman scattering (SRS) and self-phase modulation (SPM), extra-large mode area ytterbium (Yb)-doped step-index dual cladding fiber has been utilized as gain fiber in the MOPA laser system. The gain saturation effect in the power amplifier was greatly mitigated by the programmed seed signal. This pulse-shaped MOPA system can provide practical applications in many fields such as laser cleaning, paint stripping, and other applications requiring special pulse shapes.